Fisheye lens question

Just received my Sigma 15mm fisheye today. It's a rather cute piece of kit, being much smaller and lighter than either of the lenses I'm used to using. Initial tests seem sharp too, though the box was severely crushed during shipping and I'm worried about lens damage.

Here's a question for you optics nerds:

On a fisheye lens, if one points the lens at a flat surface parallel to the film plane (like the walls/tiles ala 12-24 lens tests), will the entire surface be in focus? We are talking about wide open apertures and close focusing distances here so the huge DOF of the lens doesn't count.

I tested the Sigma on a sheet of text just to see if the corners were soft wide open, and noticed that there was one circular or elliptical zone of sharp focus in the middle of the frame, which dropped off rapidly:

Is this a normal feature of fisheye lenses, ie. a non-flat plane of focus? I know that theory predicts a similar non-flat plane of focus for rectilinear lenses too, but in practice photographing a sheet of text results in having the entire sheet in focus...